{"id":{"repo_id":"vt","oai_identifier":"oai:vtechworks.lib.vt.edu:10919/71454"},"canonical_url":"https://search.dev.ndltd.org/etd/vt/oai:vtechworks.lib.vt.edu:10919/71454","repository":{"repo_id":"vt","name":"Virginia Tech","base_url":"https://vtechworks.lib.vt.edu/oai/request"},"display":{"title":"Vibrational Energies of the Hydrogen Bonds of H₃O₂⁻ and H₅O₂⁺","abstract":"We approximate the vibrational energies of the symmetric and asymmetric stretches of the hydrogen bonds of the molecules H_3O_2^- and H_5O_2^+ by applying an improvement to the standard time-independent Born-Oppenheimer approximation. These two molecules are symmetric around a central hydrogen which participates in hydrogen bonding. Unlike the standard Born-Oppenheimer approximation, this approximation appropriately scales the hydrogen nuclei differently than the heavier oxygen nuclei. This results in significantly more accurate approximations for the stretching vibrational energies, which we compare to experimental measurements.","abstract_html":"We approximate the vibrational energies of the symmetric and asymmetric stretches of the hydrogen bonds of the molecules H_3O_2^- and H_5O_2^+ by applying an improvement to the standard time-independent Born-Oppenheimer approximation. These two molecules are symmetric around a central hydrogen which participates in hydrogen bonding. Unlike the standard Born-Oppenheimer approximation, this approximation appropriately scales the hydrogen nuclei differently than the heavier oxygen nuclei. This results in significantly more accurate approximations for the stretching vibrational energies, which we compare to experimental measurements.","abstract_has_math":false,"creators":["Gamble, Stephanie Nicole"],"institution":"Virginia Tech","degree_name":"Master of Science","degree_level":"masters","degree_discipline":"Mathematics","degree_department":"Mathematics","school":null,"contributors":[],"advisors":[],"committee_chairs":["Hagedorn, George A."],"committee_members":["Crawford, T. Daniel","Valeyev, Eduard Faritovich"],"year":2016,"date_issued":"2016-06-24","date_published":"2016-06-24","updated_at":"2026-07-22T22:20:17Z","subjects":["hydrogen bond","double well","vibrational energies"],"languages":[],"rights":["In Copyright"],"rights_urls":["http://rightsstatements.org/vocab/InC/1.0/"],"identifier_entries":[{"key":"dc:identifier.other","label":"Dc Identifier Other","values":["vt_gsexam:8423"],"render_values":[{"text":"vt_gsexam:8423","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/10919/71454","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.committeechair","label":"Committee Chair","values":["Hagedorn, George A."]},{"key":"dc:contributor.committeemember","label":"Committee Member","values":["Crawford, T. Daniel","Valeyev, Eduard Faritovich"]},{"key":"dc:contributor.department","label":"Department","values":["Mathematics"]},{"key":"dc:creator","label":"Author","values":["Gamble, Stephanie Nicole"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2016-06-25T08:01:21Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2016-06-25T08:01:21Z"]},{"key":"dc:date.issued","label":"Date","values":["2016-06-24"]},{"key":"dc:publisher","label":"Institution","values":["Virginia Tech"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["masters"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Science"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["Virginia Polytechnic Institute and State University"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["hydrogen bond","double well","vibrational energies"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:rights","label":"Dc Rights","values":["In Copyright"]},{"key":"dc:rights.uri","label":"Rights URI","values":["http://rightsstatements.org/vocab/InC/1.0/"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.other","label":"Dc Identifier Other","values":["vt_gsexam:8423"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/10919/71454"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["We approximate the vibrational energies of the symmetric and asymmetric stretches of the hydrogen bonds of the molecules H_3O_2^- and H_5O_2^+ by applying an improvement to the standard time-independent Born-Oppenheimer approximation. These two molecules are symmetric around a central hydrogen which participates in hydrogen bonding. Unlike the standard Born-Oppenheimer approximation, this approximation appropriately scales the hydrogen nuclei differently than the heavier oxygen nuclei. This results in significantly more accurate approximations for the stretching vibrational energies, which we compare to experimental measurements."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["Master of Science"]},{"key":"dc:format.medium","label":"Dc Format Medium","values":["ETD"]},{"key":"dc:title","label":"Title","values":["Vibrational Energies of the Hydrogen Bonds of H₃O₂⁻ and H₅O₂⁺"]}]}],"canonical_facts":{"dc:contributor.committeechair":["Hagedorn, George A."],"dc:contributor.committeemember":["Crawford, T. Daniel","Valeyev, Eduard Faritovich"],"dc:contributor.department":["Mathematics"],"dc:creator":["Gamble, Stephanie Nicole"],"dc:date.accessioned":["2016-06-25T08:01:21Z"],"dc:date.available":["2016-06-25T08:01:21Z"],"dc:date.issued":["2016-06-24"],"dc:description.abstract":["We approximate the vibrational energies of the symmetric and asymmetric stretches of the hydrogen bonds of the molecules H_3O_2^- and H_5O_2^+ by applying an improvement to the standard time-independent Born-Oppenheimer approximation. These two molecules are symmetric around a central hydrogen which participates in hydrogen bonding. Unlike the standard Born-Oppenheimer approximation, this approximation appropriately scales the hydrogen nuclei differently than the heavier oxygen nuclei. This results in significantly more accurate approximations for the stretching vibrational energies, which we compare to experimental measurements."],"dc:description.degree":["Master of Science"],"dc:format.medium":["ETD"],"dc:identifier.other":["vt_gsexam:8423"],"dc:identifier.uri":["http://hdl.handle.net/10919/71454"],"dc:publisher":["Virginia Tech"],"dc:rights":["In Copyright"],"dc:rights.uri":["http://rightsstatements.org/vocab/InC/1.0/"],"dc:subject":["hydrogen bond","double well","vibrational energies"],"dc:title":["Vibrational Energies of the Hydrogen Bonds of H₃O₂⁻ and H₅O₂⁺"],"dc:type":["Thesis"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["masters"],"thesis:degree_name":["Master of Science"],"thesis:institution_name":["Virginia Polytechnic Institute and State University"]},"updated_at":"2026-07-22T22:20:17Z"}